Linear machinery for morphological distortion

摘要: Abstract In 1917 D'Arcy Thompson reduced the problem of comparing two homologous shapes to construction and depiction a mathematical distortion in plane. Attempts at algorithms for this computation, found mostly biological literature, ignore primacy boundary correspondence within data. One can define roughness map as extent which image centroid square deviates from images its corners; analytically, is sum squared Laplacians real imaginary parts. When data are supplied geometrically form point paris, one compute by wholly linear methods function (splined over mesh) accords with geometric homologies has least integral roughness. The necessary high-order matrix operations available numerical-analysis literature under rubric “fast Poisson solvers.” resulting explicit smooth functions lend themselves naturally diagrammatic display terms eigenstructure symmetrized strain curves principal directions.